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Robust stabilization to limit cycles of switching discrete-time affine systems using control Lyapunov functions

Abstract : This paper deals with the robust stabilization of uncertain discrete-time switched affine systems using a control Lyapunov approach and a min-switching state-feedback control law. After presenting some preliminaries on cycles and limit cycles, a constructive stabilization theorem is provided and guarantees that the solutions to the nominal closed-loop system converge to a limit cycle. These conditions are expressed in terms of simple linear matrix inequalities (LMI), whose underlying necessary conditions relax the usual one in this literature. This method is extended to the case of uncertain systems, for which the notion of limit cycle needs to be adapted. The theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature.
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Preprints, Working Papers, ...
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https://hal.laas.fr/hal-03110340
Contributor : Mathias Serieye <>
Submitted on : Thursday, January 14, 2021 - 2:57:35 PM
Last modification on : Monday, January 18, 2021 - 10:49:35 AM

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  • HAL Id : hal-03110340, version 1

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Mathias Serieye, Carolina Albea-Sanchez, Alexandre Seuret, Marc Jungers. Robust stabilization to limit cycles of switching discrete-time affine systems using control Lyapunov functions. 2021. ⟨hal-03110340⟩

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